Temperature dependent viscosity effects on laminar forced convection in the entrance region of straight ducts

A parametric investigation is carried out on the effects of temperature dependent viscosity in simultaneously developing laminar flow of a liquid in straight ducts of arbitrary but constant cross-sections. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. Different cross-sectional geometries are considered, corresponding both to three-dimensional (rectangular, trapezoidal and hexagonal) and to axisymmetric (circular and concentric annular) duct geometries. Uniform wall temperature boundary conditions are imposed on the heated/cooled walls of the ducts. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor for ducts of the considered cross-sections are presented with reference to both fluid heating and fluid cooling. Numerical results confirm that, in the laminar forced convection in the entrance region of straight ducts, the effects of temperature dependent viscosity cannot be neglected in a wide range of operative conditions.